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A185320 E.g.f. A(x) = Sum_{n>=0} a(n)*x^(2*n+1)/(2*n+1)! is inverse to f(x) = 2*arctan(x) - x. 0
1, 4, 112, 8608, 1295104, 322018816, 119597651968, 62037189087232, 42842215767801856, 38001850792907505664, 42106195262186260529152, 56992583802129636291248128, 92535374062287540141093289984, 177509548409832461509746497683456, 397176345992538727622693418988208128 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..14.

Vladimir Kruchinin, The method for obtaining expressions for coefficients of reverse generating functions, arXiv:1211.3244 [math.CO], 2012.

FORMULA

a(n) = sum(k=1..2*n, (2*n+k)!*sum(j=1..k, sum(l=0..j-1, ((-1)^(n+l+j)*sum(i=j-l..2*n-l+j, (2^i*Stirling1(i,j-l)*binomial(2*n-l+j-1,i-1))/i!))/l!)/(k-j)!)), n>0, a(0)=1.

a(n) ~ 2^(2*n+1) * n^(2*n) / (exp(2*n) * (Pi/2-1)^(2*n+1/2)). - Vaclav Kotesovec, Jan 02 2014

MATHEMATICA

Table[n!*SeriesCoefficient[InverseSeries[Series[2*ArcTan[x]-x, {x, 0, 41}], x], {x, 0, n}], {n, 1, 41, 2}] (* Vaclav Kotesovec, Jan 02 2014 *)

PROG

(Maxima) a(n):=if n=0 then 1 else sum((2*n+k)!*sum(sum(((-1)^(n+l+j)*sum((2^i*stirling1(i, j-l)*binomial(2*n-l+j-1, i-1))/i!, i, j-l, 2*n-l+j))/l!, l, 0, j-1)/(k-j)!, j, 1, k), k, 1, 2*n);

CROSSREFS

Sequence in context: A221625 A013151 A006718 * A293158 A196458 A262261

Adjacent sequences:  A185317 A185318 A185319 * A185321 A185322 A185323

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Feb 05 2012

STATUS

approved

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Last modified October 25 04:19 EDT 2021. Contains 348237 sequences. (Running on oeis4.)